Tools of the type mentioned here are known, in particular fine machining tools such as reamers and the like. When machining holes in workpieces, a relative rotational movement between tool and workpiece is realized in order to remove chips from the surface of the hole. As a rule, the tool is set into rotation and displaced in the direction of its axis of rotation with respect to a hole in the workpiece. The tool has at least one geometrically defined cutting edge, of which, the major cutting edge, is inclined in the direction of the feed movement of the tool. The minor cutting edge, which as a rule slopes in the opposite direction to the feed direction, is joined to the major cutting edge, as a result of which a taper is realized. When tools of this kind are set up, not only must the machining diameter of the tool be adjusted but also the taper. It has been established that the taper frequently changes when the diameter is adjusted and, vice versa, the required diameter is not maintained when the taper is adjusted. In order to avoid this disadvantage, in known tools, a guiding surface, which corresponds to an appropriate contact surface in the main body of the tool, is created by means of a side surface of a cutting body which incorporates the at least one geometrically determined cutting edge. In doing so, special cutting bodies are required, with which the number of available cutting edges is reduced. It is also known to accommodate cutting bodies of the kind mentioned here in receptacles, also referred to as cassettes, on which the adjusting forces for realizing the required diameter and the required taper act. This results in the disadvantage that, in the case of cassettes which swivel about a point, the taper of the at least one cutting edge changes when adjusting the machining diameter of the tool. Cassettes with two adjusting wedges, the setting of which is complicated and time-consuming, also exist.